I think you're comparing apples to oranges, at best. Both woods can be fine for a project, but they're completely different. Either will warp, depending on the cut of the wood, knots etc... Both will cup & twist, too. I'd have to say that I usually have better luck with Yellow Pine, it's inherently more stable, being denser, with a longer grain & is a lot stronger than White, so I'd use the dimensions that you'll be cutting it to for making a decision. It can split easier than the White, though. You're back to how the wood is cut & how you're going to join it & at what dimensions.
Comparing either one to Red Oak or Maple is another kettle of fish. They're hard woods, the first extremely ring porous & the other is diffusely porous. All have completely different finishing properties. How are you planning on finishing it?
Half the battle with any project is picking out the wood. I've gone with a different species simply because I couldn't get enough of one to be able to cut out enough good pieces for the amount of money I had to spend or because the design called for strength that one wood had & another didn't. Finishing is always a consideration. White Pine blotches unless you seal it well before staining. Yellow can have pockets of resin that won't take a stain well. Red Oak needs to be filled while Maple is usually perfect for staining with almost no work. Mostly, I like clear finishes because the wood is so pretty anyway. If you're painting, who cares? You might as well use plastic wood.
Jim